The problem in a WAMP server or, generally, any local server is the transfer speed between S3 and your server. There's not much you can do about it. It's MUCH more efficient using a different method to download the backup archive from S3 to your computer, e.g. CloudBerry S3 Explorer. Then just put all parts of the backup archive in the output directory of the default backup profile, by default administrator/components/com_akeeba/backup, and the use the Discover and Import feature to import the backup into your site. You can then do anything you want on that imported backup record, such as restore it.
If, however, you do not have a Joomla! site and you want to import the archive from S3 in order to restore it, it's much more efficient using a different method to download the backup archive from S3 to your computer, e.g. CloudBerry S3 Explorer. Then you just need to put the downloaded archive file(s) in your intended site's root together with kickstart.php and simply run Kickstart.
Nicholas K. Dionysopoulos
Lead Developer and Director
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